Can Six Pencils Be Arranged to Each Touch the Other Five?

  • Context: High School 
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SUMMARY

The discussion centers on the mathematical puzzle of arranging six pencils so that each pencil touches the other five. It is established that a solution exists only in three-dimensional space, as a planar arrangement fails to achieve this. Participants debate the validity of various proposed solutions, emphasizing that the pencils must not be bent or distorted. The original puzzle, adapted from Martin Gardner's work, highlights the complexities of non-planar geometry and the necessity for precise configurations.

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  • Understanding of three-dimensional geometry
  • Familiarity with Martin Gardner's puzzles
  • Basic knowledge of geometric configurations and constraints
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  • Research non-planar geometric configurations in mathematics
  • Explore Martin Gardner's original puzzles for additional context
  • Learn about the application of linear algebra in geometric problem-solving
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  • #31
gmax137 said:
The question now (nearly 3 months later) is, has @DaveE painted his bathroom yet?
Yep. Stuck on the tile though. I don't know if I should do it myself or pay someone. Apparently thinking about it harder doesn't actually work. However, it is the path of least resistance (the least usable bathroom, too). One year+ on this project, I don't think I'd make it as a remodel contractor.
 
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